On the Performance Analysis of Epidemic Routing in Non-Sparse Delay Tolerant Networks

We study the behavior of epidemic routing in a delay tolerant network as a function of node density. Focusing on the probability of successful delivery to a destination within a deadline (PS), we show that PS experiences a phase transition as node density increases. Specifically, we prove that PS exhibits a phase transition when nodes are placed according to a Poisson process and allowed to move according to independent and identical processes with limited speed. We then propose four fluid approximations to evaluate the performance of epidemic routing in non-sparse networks. An ordinary differential equation (ODE) is proposed for supercritical networks based on approximation of the infection rate as a function of time. Other ODEs are based on the approximation of the pairwise infection rate. Two of them, one for subcritical networks and another for supercritical networks, use the pairwise infection rate as a function of the number of infected nodes. The other ODE uses pairwise infection rate as a function of time, and can be applied for both subcritical and supercritical networks achieving good accuracy. The ODE for subcritical networks is accurate when density is not close to the percolation critical density. Moreover, the ODEs that target only supercritical regime are accurate.